Show that the equation I=nAvq is homogeneous with respect to units??

I = nAvq
C/s = (n/m^3)(m^2)(m/s)(C)

(m^-3) x (m^-2) x m = m^0 = 1

so m's cancel

C/s = (n)C/s

How do you proceed from here?

I have got the equation I=nAvq

Which when broken down into the units, is:
c/s = (n/m^3)(m^2)(m/s)(c)

How do I carry on from here to show that it is homogeneous/the same?

Upon googling it, I see someone on this forum asked the same thing, but after my c/s=..... step, they asked


Can you explain how I would go about after my first step? The other person said they used (m^-3) x (m^-2) x m = m^0 = 1, what does that mean and where does it come from? I am stuck after seperating it into the units of C/s = (n/m^3)(m^2)(m/s)(C)

Any help would be greatly appreciated,

Thanks

$\frac{1}{m^2} = m^{-2}$

$\frac{1}{m^3} = m^{-3}$

$\frac{1}{m^n} = m^{-n}$

i.e. eliminate the denominators so that the whole equation is on one line.

Then tidy up.

Yu should be left with C = C.

Why do you do 1/m^3 for example. Why do you do 1 divided by the units on the right hand side of the equation? And why do you not do the same to the left hand side?

Thanks

Have you not learned the basic maths rules for manipulating exponents, powers, roots etc?

You need to learn and practice these so that you can apply them to the problem.

Start with these and work through it:

http://www.bbc.co.uk/schools/gcsebitesize/maths/number/powersrootshirev1.shtml

http://www.mathcentre.ac.uk/resources/uploaded/mc-ty-indicespowers-2009-1.pdf

I have learnt those before, but I don't see why you need to say m^-2 rather than m^2

You don't need to write it out but you do need to perform the reduction nevertheless.

OK thanks. What is the reason as to why you need to perform the reduction with something as simple as m^2 to m^-2? I get that for longer equations it makes it much easier to reduce the powers, but I'm not sure why you need to in this case.

The units of I = C/s, n=m^-3 , A=m², v=m/s, q=C

so nAvq = m^-3 x m² x m/s x C

-3+2+1 = 0 so m has gone leaving C/s which is the same as the units of I.

n is the number per unit volume so has units of 1/m³ which is better written m^-3

so nAvq = m^-3 x m² x m/s x C

-3+2+1 = 0 so m has gone leaving C/s which is the same as the units of I.

In this bit:


The equation at the bottom, the -3 comes from the m^-3, the +2 comes from the m^2 and the +1 comes from m/s, but why/how does the m/s end up being +1 in that equation at the bottom? And what happens to the s in m/s? WHere does that go?

Thanks, can you just explain how m/s ends up being +1 and where the s goes? I get and understand now the -3 and +2, just not the +1.